What does this mean? How are they done? What is the difference? Is one better than the other? Why? Is one better for some applications and the other for different applications?? Does it really matter?
Let's dissect this bit by bit.
First point. You have knit a shawl, scarf, afghan, or almost anything else and have bound off the edges, you suddenly decide you want to add a border or an edging. This is when you either knit up or pick up.
Second point. To pick up, means to go around and (usually from the right side to the wrong side) insert the needle into the stitch and pull a loop through. IF you are knitting up, pick up a loop and then immediately put it onto the left needle and knit it. Repeat either across the edges you want the border or edging to be located. Be consistent. When going down the side, you tend to need 3 picked up stitches to every 4 rows or a similar ratio. When going across the end of the knitting at the cast on or bound off edge, do a stitch for stitch pick up.
Third point. Yes it matters which one you do. Picking up tends to be a looser stitch base than the knitting up. This means that the edge as you work out might look pinched or pulled together. It will be even more pronounced if there is ribbing, the opposite of ruffled edges that are not intentional. If there is a lace, it might matter less since most laces stretch. But the looser stitch base could also mean that the stitching is consistent all through the body and the edging/border but there is long stitches between the two. That would perhaps not be the design aesthetic you are going for. On the other hand, the pick up method, being looser, would make a very stretchy joining for a lace border/edging onto a lace body. Blocking would not be a problem in this situation.
Fourth point. In general, either method is acceptable and seems to be personal preference. Generally speaking. We each will pick the method that we find makes the finish we personally like. Because humans tend to be creatures of habit, we will stick with one or the other unless specifically instructed to do one or the other for a specific reason.